# I Is this a Stirling number of the second kind?

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1. Dec 27, 2017

### HAYAO

I saw this paper that talks about phonon sidebands, multiphonon relaxation, and phonon-assisted energy transfer.

I was skimming through each of the equations, but I have problem understanding the formulation of some of them, for example Equation (3.17):
$$g_{\pm }(t) = \int d\omega \begin{Bmatrix} n_{\omega }\\ n_{\omega } +1 \end{Bmatrix}exp\left ( \pm i\omega t \right )$$

If I understand correctly, the part in the braces is the Stirling numbers of the second kind. However, it doesn't make sense to me that the bottom number is larger than the top number, because that should only give zero. So is this something else?

EDIT: dear the moderators. I wasn't really sure where this thread belongs. Purely from mathematics, this thread could belong in the math section, but considering that the discussion centers around the physical aspect of a quantum mechanical phenomena, I decided to put this in this section.

2. Jan 1, 2018

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Jan 2, 2018

### Demystifier

I haven't seen the paper, but would it make sense that upper (lower) case corresponds to the plus (minus) sign?

4. Jan 4, 2018

### HAYAO

Oh, now it makes great sense. Sorry for the bum question. Thank you very much!